To write a fraction into a decimal, divide the numerator by the denominator. 75**. But for example, the fraction 3/4 means 3 ÷ 4, which equals **0. This simple rule applies to every fraction, whether it produces a terminating decimal or a repeating decimal.
Introduction
Understanding how to write a fraction into a decimal is an essential mathematics skill. A fraction such as 1/2 and the decimal 0.Now, fractions and decimals are two different ways of representing the same value. 5 describe exactly the same amount.
The most reliable method is division: the numerator becomes the number being divided, and the denominator becomes the number dividing it. More advanced learners can also use equivalent fractions, place value, or mental math when the denominator is a power of 10.
Worth pausing on this one.
What Is a Fraction?
A fraction represents a part of a whole. It has two main parts:
- The numerator, which is the top number and shows how many equal parts are being considered.
- The denominator, which is the bottom number and shows how many equal parts make up the whole.
As an example, in 5/8, the numerator is 5 and the denominator is 8. The expression 5/8 means five equal parts of a whole that has been divided into eight parts The details matter here..
The fraction bar also represents division. Therefore:
5/8 = 5 ÷ 8
This relationship is the foundation for converting any fraction into a decimal.
Method 1: Divide the Numerator by the Denominator
Step 1: Identify the numerator and denominator
In the fraction 7/8:
- 7 is the numerator.
- 8 is the denominator.
Step 2: Rewrite the fraction as a division problem
7/8 = 7 ÷ 8
Step 3: Perform long division
Because 8 is larger than 7, place a decimal point after 7 and add zeros:
7.000 ÷ 8
Divide as follows:
- 8 goes into 70 eight times. Write 8 after the decimal point.
- Eight times 8 is 64. Subtract 64 from 70 to get 6.
- Bring down 0 to make 60.
- 8 goes into 60 seven times. Write 7.
- Eight times 7 is 56. Subtract 56 from 60 to get 4.
- Bring down another 0 to make 40.
- 8 goes into 40 five times exactly.
Thus:
7 ÷ 8 = 0.875
So, 7/8 = 0.875.
More examples
| Fraction | Division | Decimal |
|---|---|---|
| 1/2 | 1 ÷ 2 | 0.Day to day, 5 |
| 1/4 | 1 ÷ 4 | 0. On the flip side, 75 |
| 2/5 | 2 ÷ 5 | 0. Worth adding: 25 |
| 3/4 | 3 ÷ 4 | 0. 4 |
| 5/8 | 5 ÷ 8 | 0.625 |
| 9/16 | 9 ÷ 16 | 0. |
Method 2: Use Equivalent Fractions with Powers of 10
Some fractions can be converted quickly by changing the denominator into 10, 100, 1,000, or another power of 10. This method uses place value.
Example: Convert 3/4 to a decimal
The denominator 4 must become 100. Multiply both the numerator and denominator by 25:
3/4 = (3 × 25)/(4 × 25) = 75/100
A fraction with a denominator of 100 can be written directly in decimal form:
75/100 = 0.75
Example: Convert 7/20 to a decimal
Multiply the numerator and denominator by 5:
7/20 = (7 × 5)/(20 × 5) = 35/100
Therefore:
35/100 = 0.35
This method is especially useful when the denominator can easily be changed into 10, 100, or 1,000.
Method 3: Use Mental Math for Common Fractions
Memorizing common fraction-decimal relationships can make conversions faster Simple, but easy to overlook..
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/3 | 0.333… |
| 1/4 | 0.25 |
| 1/5 | 0.Plus, 2 |
| 1/8 | 0. 125 |
| 1/10 | 0.Which means 1 |
| 1/20 | 0. 05 |
| 1/25 | 0.04 |
| 3/4 | 0.75 |
| 2/3 | 0. |
As an example, 3/5 can be recognized as three groups of 1/5. Since 1/5 = 0.2, then:
3/5 = 3 × 0.2 = 0.6
Similarly, 7/10 means seven tenths.
